Diffusion Theory of Nonequilibrium Dissociation and Recombination

The coupled vibration—dissociation—recombination process for molecules and atoms has been examined. Techniques for solving the appropriate master equations for both quantum (discrete) and classical (continuous) models are given. It is shown that the process is most easily treated classically and that in this case the master equation can be reduced to an equivalent diffusion equation. It is assumed that, after an initial vibration transient, during which reactions are negligible, the process may be treated using the steady-state approximation. During the steady-state phase, the usual phenomenological rate equations are valid and the ratio of the forward and reverse rate constants is the equilibrium constant, though the individual rate constants are depressed below their equilibrium values. Comparison of the results with other theoretical work shows general agreement for similar models; comparison with shock-tube experiments on molecular dissociation and stellarator experiments on ionic recombination is encouraging.